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Finding the Third Proportional to 262,642 and 407,463

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Solution

The third proportional to 262,642 and 407,463 is: 632,138.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,642 : 407,463 = 407,463 : x
  2. Step 2: Convert to fraction form
    262,642/407,463 = 407,463/x
  3. Step 3: Cross multiply
    262,642x = 407,463 × 407,463
  4. Step 4: Simplify right side
    262,642x = 166,026,096,369
  5. Step 5: Solve for x
    x = 166,026,096,369/262,642
  6. Step 6: Final answer
    x = 632,138.41

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.